Improvement of Stability Transformation Method for First Order Reliability Analysis

Document Type : مقاله کوتاه

Author

• Behrooz Keshtegar

University of Zabol

10.22067/fum-mech.v28i2.42636

Abstract

The stability transformation method (STM) of chaos feedback control is a simple and efficient approach to implement the convergence control of the first order reliability method (FORM). The robustness and efficiency of the STM are depended on selected parameters of this algorithm such that involuntary matrix and step size in structural reliability analysis. When involuntary matrix and step size are inappropriately selected, the STM iterative formula can be prematurely and slowly converged. In this paper, the STM scheme was improved based on a simple dynamical step size and the involuntary matrix equals to unit matrix. The proposed dynamical step size can be computed using the new and previous results of the FORM iterative formula. The efficiency and robustness of improved STM was compared with the STM and finite-step length methods from five numerical and mechanical examples taken through the literature. The results impales that the improved STM not only ensured the numerical stability of nonlinear mechanical problems but also is more efficient than the STM to approximate the failure probability.

Keywords

• First order reliability method
• stability transformation method: dynamical step size

---

References

1. Hasofer, A.M. and Lind, N.C., "Exact and invariant second moment code format", Journal of the Engineering Mechanics Division, Vol. 111, No. 21, pp. 111-121, (1974).

2. Elegbede. C., "Structural reliability assessment based on particles swarm optimization", Structural Safety, Vol. 27, No. 2, pp. 171–186, (2005).

3. Keshtegar, B. and Miri, M., "Introducing Conjugate gradient optimization for modified HL-RF method", Engineering Computations, Vol. 31, No. 4, pp. 775-790, (2014).

4. Rackwitz, R. and Fiessler, B., "Structural reliability under combined load sequences", Computers and Structures, Vol. 9, No. 8, pp. 489-494, (1978).

5. Liu, P.L. and Kiureghian, A.D., "Optimization algorithms for structural reliability", Structural Safety, Vol. 9, No. 3, pp. 161-178, (1991).

6. Santosh. T. V., Saraf. R.K., Ghosh. A.K. and Kushwaha. H.S., "Optimum step length selection rule in modified HL-RF method for structural reliability", International Journal of Pressure Vessels Piping, Vol. 83, No. 10, pp. 742–748, (2006).

7. Yang, D., "Chaos control for numerical instability of first order reliability method", Communications in Nonlinear Science and Numerical Simulation, Vol. 5, No. 10, pp. 3131-3141, (2010).

8. Gong, J.X. and Yi, P., "A robust iterative algorithm for structural reliability analysis", Structural and Multidisciplinary Optimization, Vol. 43, No. 4, pp. 519–527, (2011).

9. Keshtegar, B. and Miri, M., "An enhanced HL-RF Method for the computation of structural failure probability based on relaxed approach", Civil Engineering Infrastructures, Vol. 1, No. 1, pp. 69-80, (2013).

10. کشته‌گر، بهروز، میری، محمود، «ارائۀ روشی جدید برای ارزیابی قابلیت اعتماد سازه‌ها»، مجلۀ مدل‌سازی در مهندسی، سال 12، شمارۀ 36، صص 42-29، (1393).

11. Yang, D., Li, G. and Cheng, G., "Convergence analysis of first order reliability method using chaos theory", Computers and Structures, Vol. 84, Vol. 8-9, pp. 563–571, (2006).

12. Wang, L.P. and Grandhi, R.V., "Efficient safety index calculation for structural reliability analysis", Computers and Structures, Vol. 52, No. 1, pp. 103–111, (1994).

13. Schmelcher, P. and Diakonos, F.K., "General approach to the localization of unstable periodic orbits in chaotic dynamical systems", Physical Review Letters, Vol. 57, No.1, pp. 2739-2754, (1998).

14. Yang, D.X. and Yi, P., "Chaos control of performance measure approach for evaluation of probabilistic constraints", Structure Multidisciplinary Optimization, Vol. 38, No. 1, pp. 83-92, (2009).

15. Kiureghian, A.D. and Stefano, M.D., "Efficient algorithm for second-order reliability analysis", Journal of Engineering Mechanics, Vol. 117, No. 12, pp. 2904-2923, (1991).